2. To calculate multiplication of matrices
To interpret properties of multiplication
To validate properties of multiplication
Learning Outcomes
3. Matrices
Let's multiply two matrices!
What
does it
mean?
The product of two matrices A and B is defined if the number of columns
of A is equal to the number of rows of B.
4. Matrices
Let's multiply two matrices!
What
does it
mean?
The product of two matrices A and B is defined if the number of columns
of A is equal to the number of rows of B.
Let A = [aij] be an m × n matrix and B = [bjk] be an n × p matrix.
5. Matrices
Let's multiply two matrices!
What
does it
mean?
The product of two matrices A and B is defined if the number of columns
of A is equal to the number of rows of B.
Let A = [aij] be an m × n matrix and B = [bjk] be an n × p matrix.
Then the product of the matrices A and B is the matrix C of order m × p.
6. Matrices
Let's multiply two matrices!
Let's take
an
example!
The product of two matrices A and B is defined if the number of columns
of A is equal to the number of rows of B.
Let A = [aij] be an m × n matrix and B = [bjk] be an n × p matrix.
Then the product of the matrices A and B is the matrix C of order m × p.
To get the (i, k)th element cik of the matrix C, we take the ith row of A and
kth column of B, multiply them elementwise and take the sum of all these
products.
9. Matrices
Let's multiply two matrices!
Let's
illustrate
it!
If C= , D = , then CD =
This is a 2 × 2 matrix in which each entry is the sum of the products across
some row of C with the corresponding entries down some column of D.
19. To calculate multiplication of matrices
To interpret properties of multiplication
To validate properties of multiplication
Learning Outcomes
How confident do you feel?
20. To calculate multiplication of matrices
To interpret properties of multiplication
To validate properties of multiplication
Learning Outcomes
How confident do you feel?
21. The multiplication of matrices possesses the following properties, which
we state without proof.
Matrices
Let's multiply two matrices!
22. The multiplication of matrices possesses the following properties, which
we state without proof.
1. The associative law: For any three matrices A, B and C.
We have (AB) C = A (BC), whenever both sides of the equality are defined.
Matrices
Let's multiply two matrices!
What
does it
mean?
23. The multiplication of matrices possesses the following properties, which
we state without proof.
1. The associative law: For any three matrices A, B and C.
We have (AB) C = A (BC), whenever both sides of the equality are defined.
2. The distributive law: For three matrices A, B and C.
(i) A (B+C) = AB + AC
Matrices
Let's multiply two matrices!
What
does it
mean?
24. The multiplication of matrices possesses the following properties, which
we state without proof.
1. The associative law: For any three matrices A, B and C.
We have (AB) C = A (BC), whenever both sides of the equality are defined.
2. The distributive law: For three matrices A, B and C.
(i) A (B+C) = AB + AC (ii) (A+B) C = AC + BC,
whenever both sides of equality are defined.
Matrices
Let's multiply two matrices!
What
does it
mean?
25. The multiplication of matrices possesses the following properties, which
we state without proof.
1. The associative law: For any three matrices A, B and C.
We have (AB) C = A (BC), whenever both sides of the equality are defined.
2. The distributive law: For three matrices A, B and C.
(i) A (B+C) = AB + AC (ii) (A+B) C = AC + BC,
whenever both sides of equality are defined.
3. The existence of multiplicative identity: For every square matrix A,
there exist an identity matrix of same order such that IA = AI = A.
Matrices
Let's multiply two matrices!
26. To calculate multiplication of matrices
To interpret properties of multiplication
To validate properties of multiplication
Learning Outcomes
How confident do you feel?
27. To calculate multiplication of matrices
To interpret properties of multiplication
To validate properties of multiplication
Learning Outcomes
How confident do you feel?
28. If A = , B = and C = ,find A(BC), (AB)C and show that
(AB)C = A(BC).
Matrices
Let's verify the properties!
Let's
solve it!
29. If A = , B = and C = . Calculate AC, BC and (A + B)C.
Also, verify that (A + B)C = AC + BC.
Matrices
Let's verify the properties!
Let's
solve it!
48. To calculate multiplication of matrices
To interpret properties of multiplication
To validate properties of multiplication
Learning Outcomes
How confident do you feel?
49. To calculate multiplication of matrices
To interpret properties of multiplication
To validate properties of multiplication
Learning Outcomes
How confident do you feel?
51. Matrices
Learning Activity
In a legislative assembly election, a political group hired a public relations firm to
promote its candidate in three ways: telephone, house calls, and letters. The cost per
contact (in paise) is given in matrix A as:
The number of contacts of each type made in two cities X and Y is given by:
Find the total amount spent by the group in the two cities X and Y.
Editor's Notes
An overview of the content of the lesson
Must be in the form of a question where appropriate
Students should be able to answer the question at the end - either fully, partly or in a way that demonstrates they understand what gaps in their knowledge they need to address
Verbs such as to understand / to know / to gain confidence / to learn
Ask students to give the question a go and point out that, at the end of the lesson, they should be able to answer fully
Measurable outcomes that students can demonstrate and self-assess against
Must be written using Bloom’s taxonomy verbs
Verbs based on students ability and pitch of lesson
It must be clear that students understand the outcomes before moving on
Make an activity of this slide:
Ask students to read this aloud
Ask them to paraphrase
Ask that they explain what they mean
Ask what they already know related to these outcomes
There may be as few as 2 outcomes, or max 4
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Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
The next slides should be focused on achieving first outcome
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The next slides should be focused on achieving first outcome
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The next slides should be focused on achieving first outcome
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The next slides should be focused on achieving first outcome
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The next slides should be focused on achieving first outcome
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The next slides should be focused on achieving first outcome
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The next slides should be focused on achieving first outcome
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The next slides should be focused on achieving first outcome
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The next slides should be focused on achieving first outcome
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The next slides should be focused on achieving first outcome
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The next slides should be focused on achieving first outcome
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Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
Revisit the first outcome and use the polling function to allow students to privately self-assess
You may feel that the students do not need privacy to self-assess and in this instance, the chat box may be used
Polling must be used until you can fully assess their confidence to use the chat box and express honesty
If students self-assess as a 4/5, ensure that you are fully confident in their assessment
Ask questions
Ask for examples
Students to ask each other questions
If a few students self-assesses as a 3, but others as a 4/5, discretely ask the higher ones to give examples and to explain their achievement/understanding
If all students are a 3 or below, do not move on. Move to a blank page at the end of the presentation and use as a whiteboard to further explain
If students are ½, go back to the beginning
Always ask students what the gaps are and help them to identify these in order to promote metacognition
1. The outcome changes colour when achieved to the same colour as the objective to demonstrate the connection, progress and what happens next
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The next slides should be focused on achieving first outcome
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The next slides should be focused on achieving first outcome
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The next slides should be focused on achieving first outcome
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The next slides should be focused on achieving first outcome
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As previously.
As previously.
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The next slides should be focused on achieving first outcome
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The next slides should be focused on achieving first outcome
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The next slides should be focused on achieving first outcome
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The next slides should be focused on achieving first outcome
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The next slides should be focused on achieving first outcome
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The next slides should be focused on achieving first outcome
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The next slides should be focused on achieving first outcome
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The next slides should be focused on achieving first outcome
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The next slides should be focused on achieving first outcome
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As previously.
As previously.
An overview of the content of the lesson
Must be in the form of a question where appropriate
Students should be able to answer the question at the end - either fully, partly or in a way that demonstrates they understand what gaps in their knowledge they need to address
Verbs such as to understand / to know / to gain confidence / to learn
Ask students to give the question a go and point out that, at the end of the lesson, they should be able to answer fully
The next slides should be focused on achieving first outcome
Make reference to the outcome in the teaching
Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge